It has been repeatedly demonstrated that questionnaires are not a reliable method for assessing food intake. For example, in an analysis of some 63,000 subjects in the NHNAES, roughly 59% of men and 67% of women reported intakes that were physiologically implausible.

Even if a giving few surveys were a reliable scientific method, it doesn't appear that the authors controlled for the foods that tend to be eaten with red or processed meats in western countries, like fried foods, high-sugar sauces, soft drinks, and other ultra-processed foods. In fact, so far as I can tell, the paper does not contain the words "sugar" or "processed food." For some reason they adjusted the red and processed meat analyses for milk, cheese, and fiber from bread and cereal, but not for sugar intake, sweetened beverage intake, or ultra-processed food intake. They also found that the effect size was attenuated by adjusting for smoking, alcohol consumption, and waist circumference, and that the red meat association was not as strong after that. (Processed meat still was.) They also did not adjust results for income, which seems like a big problem.